Methods of and Apparatuses for Identifying Geological Characteristics in Boreholes

ABSTRACT

A method of detecting an edge of a geological characteristic in a borehole comprises, in respect of an image log of a length of a borehole, carrying out the steps of a gradient-based edge detection method, a phase congruence-based edge detection method or a combination of such methods as preliminary, pre-processing stages. Subsequent steps of the method may include operating a relatively computationally simple process to identify sinusoids among detected edge features; and a relatively computationally complex process for parameterizing the thus-identified sinusoids.

CROSS-REFERENCE TO RELATED APPLICATIONS

This application is a divisional of U.S. application Ser. No.13/894,029, filed 14 May 2013, which is incorporated herein by referenceand which claims the benefit under 35 U.S.C. §119(a) to U.K. Appl. No.GB 1304304.7, filed 11 Mar. 2013.

FIELD OF THE DISCLOSURE

The invention relates to methods of and apparatus for identifyinggeological characteristics in boreholes.

BACKGROUND OF THE DISCLOSURE

A geological formation may be penetrated by a borehole for the purposeof assessing the nature of, or extracting, a commodity of commercialvalue that is contained in some way in the formation. Examples of suchcommodities include but are not limited to oils, flammable gases,tar/tar sands, various minerals, coal or other solid fuels, and water.

When considering the assessment and/or extraction of such materials thelogging of geological formations is, as is well known, economically anextremely important activity.

Virtually all commodities used by mankind are either farmed on the onehand or are mined or otherwise extracted from the ground on the other,with the extraction of materials from the ground providing by far thegreater proportion of the goods used by humans.

It is extremely important for an entity wishing to extract materialsfrom beneath the ground to have as good an understanding as possible ofthe conditions prevailing in a region from which extraction is to takeplace.

This is desirable partly so that an assessment can be made of thequantity and quality, and hence the value, of the materials in question;and also because it is important to know whether the extraction of suchmaterials is likely to be problematic.

The acquisition of such data typically makes use of techniques of wellor borehole logging. Logging techniques are employed throughout variousmining industries, and also in particular in the oil and gas industries.The invention is of benefit in well and borehole logging activitiespotentially in all kinds of mining and especially in the logging ofreserves of oil and gas.

In the logging of oil and gas fields (or indeed geological formationscontaining other fluids) specific problems can arise. Broadly statedthis is because it is necessary to consider a geological formation thattypically is porous and that may contain a hydrocarbon-containing fluidsuch as oil or natural gas or (commonly) a mixture of fluids only onecomponent of which is of commercial value.

This leads to various complications associated with determining physicaland chemical attributes of the oil or gas field in question. Inconsequence a wide variety of well logging methods has been developedover the years. The logging techniques exploit physical and chemicalproperties of a formation usually through the use of a logging tool orsonde that is lowered into a borehole formed in the formation bydrilling.

Broadly, in most cases the tool sends energy into the formation anddetects the energy returned to it that has been altered in some way bythe formation. The nature of any such alteration can be processed intoelectrical signals that are then used to generate logs (i.e. graphicalor tabular representations, or datasets, containing much data about theformation in question).

An example of a logging tool type is the so-called multi-padmicro-resistivity borehole imaging tool, such as the tool 10 illustratedin transversely sectioned view in FIG. 1. In this logging tool acircular array of (in the example illustrated) eight pads 11 each inturn supporting typically two lines of surface-mounted resistivityelectrodes referred to as “buttons” 12 is supported on a series ofcaliper arms 13 emanating from a central cylinder 14. During use of thetool 10 the arms 13 press the buttons 12 into contact with the veryapproximately cylindrical wall of a borehole. The borehole is normallyfilled with a fluid (such as a water-based mud) that if conductiveprovides an electrical conduction path from the formation surroundingthe borehole to the buttons.

Many variants on the basic imaging tool design shown are known. In somemore or fewer of the pads 11 may be present. The numbers and patterns ofthe buttons 12 may vary and the support arms also may be of differingdesigns in order to achieve particular performance effects. Sometimesthe designers of the tools aim to create e.g. two parallel rows ofbuttons located on the pad one above the other in use. The buttons inthe lower row are offset slightly to one side relative to theircounterparts in the row above. When the signals generated by the buttonsare processed the outputs of the two rows of buttons are in effect lainover one another. As a result the circumferential portion of theborehole over which the buttons 12 of a pad 11 extend is logged asthough there exists a single, continuous, elongate electrode extendingover the length in question.

Another type of resistivity logging tool is employed during so-calledlogging while drilling (LWD) operations. This logging tool may includeonly a single button.

In general in operation of a tool such as resistivity tool 10 electricalcurrent generated by electronic components contained within the cylinder14 spreads into the rock and passes through it before returning to thepads 11. The returning current induces electrical signals in the buttons12.

Changes in the current after passing through the rock may be used togenerate measures of the resistivity or conductivity of the rock. Theresistivity data may be processed according to known techniques in orderto create (typically colored) image logs that reflect the composition ofthe solid and fluid parts of the rock. These image logs convey much datato geologists and others having the task of visually inspecting andcomputationally analyzing them in order to obtain information about thesubterranean formations.

In use of a tool such as that shown in FIG. 1 the tool is initiallyconveyed to a chosen depth in the borehole before logging operationscommence. The deployed location may be many thousands or tens ofthousands of feet typically but not necessarily below, and in any eventseparated by the rock of the formation from, a surface location at whichthe borehole terminates.

Various means for deploying the tools are well known in the mining andoil and gas industries. One characteristic of many of them is that theycan cause a logging tool that has been deployed as aforesaid to be drawnfrom the deployed location deep in the borehole back towards the surfacelocation. During such movement of the tool it logs the formation,usually continuously. As a result the image logs may extend continuouslyfor great distances.

Generally the logging tool is conveyed to the depth at which loggingcommences supported on wireline, i.e. strengthened cable that is capableof both supporting the mass of the logging toolstring (that may beseveral tens or even hundreds of kilograms) and conveying electricalsignals between the logging tool and a surface location. Thus thefunctions of wireline, that are in themselves well known in the loggingart, include suspending the logging tool while it is being deployed foruse; withdrawing the tool towards a surface location during use;transmitting electrical or electronic commands to the toolstring toeffect chosen operations; and telemetering data, from which the logs areconstructed, from the tool to the surface location while logging occurs.

Other designs of logging tool are autonomous in the sense of not beingpermanently connected to a surface location by wireline. Such toolsinclude on-board power sources and memory devices. As a result they canbe conveyed to downhole locations for example shielded within drillpipeand then exposed at the end of a length of drillpipe so as to log aformation surrounding the borehole while the drillpipe is withdrawn to asurface location. Such types of logging tool do not telemeter data inreal time and instead store it in the on-board memory devices fordownloading after retrieval of the logging tool to a surface location.

SUMMARY OF THE DISCLOSURE

The invention is of utility in relation to all the types of imaging tooloutlined above.

Furthermore the invention is of benefit in the processing of image logsthat instead of being generated by an electrical (resistivity) loggingtool are generated by an acoustic device, or by combinations ofresistivity and acoustic devices. The characteristics of image logsproduced by acoustic logging tools are sufficiently similar to those ofresistivity image logs as to permit this. For economy herein however theremainder of this document refers chiefly to logs produced usingresistivity image logging tools notwithstanding the applicability of themethods of the invention to image log data produced using acousticlogging tools.

One characteristic of image logs is that notwithstanding in some tooldesigns a large number of buttons of the type described above the logsare discontinuous in the direction around the borehole. This is becausedeployment of the arms on which the pads are supported gives rise togaps between the pad ends at which no log data can be recorded. Also, asnoted, in some logging tool designs very few buttons indeed are present.

The inventors have devised a number of advanced techniques for fillingin such gaps in the coverage of imaging tools. Following processing ofan image log to compensate for discontinuities of the kind described, orsometimes in cases in which no filling in of this kind takes place, anaspect of particular interest to log analysts and geoscientists is thecorrect identification of sinusoids.

Sinusoids are often of very considerable significance because a planethat is intersected by a borehole at any orientation other thanorthogonally produces a sinusoidal pattern in an image log. This isbecause, as is well known in geometry, a plane intersecting a hollowcylinder produces a sinusoid in the rendering of the cylinder as atwo-dimensional sheet. Such rendering in essence is part of the processof producing a graphical image log, in which the three-dimensionalborehole is portrayed by way of a two-dimensional (usually rectangular)image.

Geological features such as fractures and layer edges, that areimportant when assessing for example the boundaries of a productive partof a subterranean formation or potential problems in removing valuablematerial to a surface location, frequently give rise to sinusoids. Thecorrect identification of sinusoids therefore is very important whenanalyzing image logs.

Hitherto the most common method of identifying sinusoids has involvedthe displaying of colored images of the logs and human assessment, byeye, of the visible features.

Humans are good at visually interpreting patterns so the recognition ofsinusoids in this fashion can be achieved with acceptable reliability.Any process of inspecting a log, that as indicated might extend forhundreds or thousands of feet, however is very time-consuming. This ispartly because the length of the log may simply make this a lengthyprocess. Also there may be a very large number of sinusoids, orpotential sinusoids, to assess.

Aside from the fact that log analysis time is expensive in somesituations the rapid identification of geological features may onoccasion be of considerable economic or even safety-related importance.

Attempts have been made to automate the recognition of certaingeological features in image logs, but these have been of limitedutility in identifying sinusoids. One reason for this is that thesinusoids while usually readily recognizable to a human analyst arealmost never perfect. On the contrary they are frequently distorted,interrupted and skewed.

Skewing and distortion arise in part because the boreholes in whichlogging takes place are rarely truly cylindrical. The rendering in atwo-dimensional image of a plane that intersects a non-cylindricalfigure is not a perfect sinusoid. Machine vision systems hitherto havebeen unreliable at recognizing such imperfect sinusoids.

Furthermore the creation of perfect sinusoids would depend on thelogging tool being withdrawn towards an uphole location, during logging,at a constant speed. The fact that for a variety of reasons this doesnot often happen means that the vertical scale of the apparent sinusoidmay vary from place to place. As a result the sinusoid often cannot bemodeled by a single function as would be ideal for existingsoftware-based recognition methods and equipment.

Yet a further problem is that image logs can be very “noisy” in terms ofspurious image features and similar defects.

Other causes of imperfection are also known to log analysts andgeologists.

The invention is of utility in relation to all the types of imaging tooloutlined above. Furthermore the invention is of benefit in theprocessing of image logs that instead of being generated by anelectrical (resistivity) logging tool are generated by an acousticdevice, or by combinations of resistivity and acoustic devices. Thecharacteristics of image logs produced by acoustic logging tools aresufficiently similar to those of resistivity image logs as to permitthis. For economy herein however the remainder of this document referschiefly to logs produced using resistivity image logging toolsnotwithstanding the applicability of the methods of the invention toimage log data produced using acoustic logging tools.

An aim of the invention is to improve the extent to which automated ormachine-driven sinusoid assessments in image logs can be completed.

The inventors have developed improved machine recognition regimes,methods and apparatuses, as defined herein, for identifying sinusoids inimage logs. The inventors furthermore have recognized that the improvedmachine techniques they have developed are themselves more effective ifthe image log data are pre-processed before the improved imagerecognition techniques are applied.

The inventors have discovered that a gradient-based approach issuccessful as such a pre-processing step. To this end in a first aspectof the invention there is provided a method of detecting an edge of ageological characteristic in a borehole comprising, in respect of animage log of a length of a borehole, carrying out the steps of agradient-based edge detection method.

More specifically the gradient-based edge detection method is adifferential geometric multi-scale method.

This method optionally includes defining as a scale-space edge a set ofconnected points in a scale-space at which:

-   -   a. the gradient magnitude assumes a local maximum in the        gradient direction; and    -   b. a normalized measure of the strength of the edge response is        locally maximal over plural scales.

The gradient-based approach in essence seeks to identify and locatesharp or pronounced discontinuities in the image log, that manifestthemselves as abrupt changes in pixel intensity.

Preferably the scale levels employed for detection of relatively sharperedges are finer than the scale levels employed for detection ofrelatively less sharp edges. This is an automatic consequence of theapproach adopted of suppressing non-local maxima as described hereinbelow.

In order to determine the fineness or coarseness of the scale applied,the method preferably includes calculating a diffuseness estimate ateach of a plurality of points along the said edge. The method alsooptionally includes, as noted, suppressing non-local maxima.

As an adjunct or alternative to the gradient-based edge detectiontechnique defined hereinabove the inventors additionally haveestablished that a phase congruency approach also is a successfulpre-processing method.

To this end therefore in a broad second aspect of the invention there isprovided a method of detecting an edge of a geological characteristic ina borehole comprising the steps of, in respect of an image log of alength of a borehole, identifying locations at which the phasecongruency of components of a signal representative of data constitutingthe log or part thereof is maximal; and, in respect of such locations,characterizing them as one or more edges of geological characteristics.

Thus the second broad aspect of the invention involves a further edgedetection technique as outlined. One significant advantage of thisaspect of the invention is that it reduces the number of featuresfalsely identified as sinusoids, by eliminating from furtherconsideration those that are not true edge features of the kind thatcharacterize sinusoids in image logs.

The inventors have found that the use of phase congruency at specificlocations is an extremely reliable way of identifying edges that areassociated with sinusoids.

The inventors in particular have found that the phase congruencytechnique is especially beneficial when carried out on image log datathat have been the subject of gradient-based pre-processing inaccordance with the first aspect of the method of the invention. Howeverthe phase congruency technique defined herein can be carried out as aninitial pre-processing technique or even as the sole pre-processingtechnique within the scope of the invention.

Preferably the method includes generating a plurality of Fouriertransforms respectively corresponding to the said components; comparingphase information in the Fourier transforms corresponding to a pluralityof locations in the image log; and at locations where the phaseinformation converges or is the same, characterizing such locations asone or more edges of geological characteristics.

This aspect of the method of the invention takes advantage of the natureof a Fourier transform in permitting analysis of phase informationwithout considering amplitude information. This makes the pre-processingsteps of the method highly robust to noise in the image log data.

In more detail the method includes determining the phase congruency ofthe components of the said signal at a location x through operation ofthe Fourier series expansion function

${{PC}(x)} = {\max_{{\overset{\_}{\varphi}{(x)}} \in {\lbrack{0,{2\pi}}\rbrack}}\frac{\sum\limits_{n}{A_{n}{\cos \left( {{\varphi_{n}(x)} - {\overset{\_}{\varphi}(x)}} \right)}}}{\sum\limits_{n}A_{n}}}$

wherein:PC(x) is the phase congruency of the components at location x;A_(n) represents the amplitude of the Fourier transform of the nth saidcomponent; andΦ_(n)(x) represents the local phase of the Fourier transform of the nthsaid component at location x and wherein the value of φ(x) thatmaximises this function is the amplitude weighted mean local phase angleof all the Fourier transforms of the said components at location x, suchthat a locally maximal value of phase congruence occurs where theamplitude weighted variance of local phase angles, relative to theamplitude weighted local phase, is minimal.

This approach is computationally efficient and may be completed quicklyin order to reduce the population of features in the image log requiringfurther treatment to identify them as sinusoids.

As an optional adjunct to the foregoing pre-processing steps the methodof the invention includes searching for peaks in a local luminanceenergy function that is proportional to phase congruency in accordancewith the relation:

E(x)=PC(x)Σ_(n) A _(n),

whereby to obtain a measure of phase congruency that is independent ofthe amplitudes (which are contrast-invariant) of individual said Fouriertransforms.This approach to the identification of locations of maximal phasecongruency is particularly suited to image logs in which luminanceenergy is readily measurable; and moreover is computationally simplerthan the approach based on the Fourier series as set out above.

Preferably the local luminance energy function E(x) is defined for aone-dimensional luminance profile l(x) as

E(x)=√{square root over (F ²(x)+H ²(x))}{square root over (F ²(x)+H²(x))}

wherein:

F(x) is the signal l(x) following removal of its DC component; and

H(x) is the Hilbert transform of F(x).

In this aspect of the method of the invention F(x) and H(x) preferablyare approximated by convolving l(x) with a pair of quadrature filters.Quadrature filters are known per se in the context of visual perceptionmodeling, but according to the inventors' understanding they have nothitherto been used in the determination of edges in image logs.

The techniques of non-local maxima suppression differ depending onwhether the pre-processing is of the phase congruency type or thegradient determination type defined above.

In the case of phase-based image pre-processing preferably the non-localmaxima suppression technique includes using an orientation imageresulting from the steps of any of claims 7 to 12 hereof to generatefeature-normal orientation angles in respect of edge features; employinga bi-linear interpolation algorithm to estimate image intensity valuesat real-value pixel locations on either side of selected pixels of theimage log in order to determine whether the selected pixels are localmaxima; and if not, suppressing the selected pixels.

Conveniently the method also includes performing hysteresis thresholdingof the image log.

Preferably the hysteresis thresholding includes categorizing all firstpixels having grey values resulting from practicing the steps of thesecond aspect of the invention less than a threshold T1 as representingedges; and categorizing all further pixels connected to the first pixelsand having values greater than a threshold T2 also as representingedges. The use of grey values is a consequence of the phase domainprocessing. The output at this stage is a binary (0,1) image.

Preferably the method includes in respect of any square pattern of ninepixels (where the targeted pixel is in the center) categorized asrepresenting edges, disregarding the value of the center pixel.

The method also optionally includes carrying out morphological cleaningof pixels by disregarding the values of pixels on the boundaries ofobjects based on a morphological component analysis of selected parts ofthe image.

If the method of determining the presence of edge features involves agradient-based approach as set out herein the steps of non-local maximasuppression preferably involve the steps of applying a break to one ormore non-monotonic bends in the image log; applying break branches tothe result of applying breaks; and applying a cleaning filter to theresulting data.

The different processes carried out after gradient-based edge detectionare, in more detail:

-   -   1. Removal of any vertical features resulting from problems of        pad normalization, which could introduce unwanted vertical        lines.    -   2. Application of a “Lindeberg” edge algorithm again as it        provides well connected single pixel thick edges. The        connectivity of the edges is very important as it enables a        determination of how each edge or combination of more than one        edge can be fitted by a sine wave. When the edges are broken        into smaller parts, there is a very large number of possible        combinations of these edge fragments which must be examined by        the code to see how well they fit a sine wave.    -   3. Breaking of any edges that start to bend back on themselves        in the x direction. Hence, all edges after this stage are        “monotonic”. This stage is required in cases where a single edge        has been fitted to two separate sine curves in the data, and        also serves to break up the background non sine wave edge        content into shorter lengths that allows most of them to be        removed in stage 5.    -   4. Removal of any pixels which are connected to more than two        other pixels. This stage is required to ensure that all edges        consist of single lines (i.e. there are no branches). This        simplifies the processing and again addresses the case where an        edge follows two separate sine curves.    -   5. Seeking to remove unwanted edges which are due to edge        content in the background texture. This stage simplifies the        processing and reduces the likelihood of false positives.

The steps of the method of the invention defined thus far amount to(relatively quickly performed) pre-processing activities, as noted. Oncethese are complete to the extent necessary depending on the kind of edgedetection technique adopted the identification and, followingidentification, parameterizing of sinusoids becomes possible.

Estimating of sine waves therefore then occurs. A list of all of theedges found in the input image is first acquired. The algorithm thenproceeds according to a third aspect of the invention in which a methodof identifying sinusoidal geological characteristics in a boreholecomprises the steps of, in respect of an image log of a length of aborehole, employing a relatively computationally simple technique foridentifying the presence of sinusoids among detected edge features; andsubsequently applying a relatively computationally complex technique fordetermining the parameters of sinusoids identified using the relativelycomputationally simple technique.

Each edge in the list which covers most of the width of the image (athreshold of 75% currently being preferred) is first considered. Thesine wave parameters are estimated for this edge, and if the error isbelow the acceptance threshold, this sine wave is accepted. Otherwise,the edge is discarded.

For the avoidance of doubt the invention extends to a method asaforesaid when carried out on image log data processed in accordancewith the methods of any of claims 1 to 20 hereof to isolate datarepresentative of edge features.

In more detail the method of the invention includes searching forcounterpart edge features in respective locations spaced approximatelyit radians apart in the image log.

This aspect of the method takes advantage of the character of a sinewave generated by intersection of a plane with a cylinder in repeatingevery 2π radians (360°). This means that every π radians (180°) exceptat the point of crossing its horizontal axis a sine wave is of equalmagnitude and opposite sign.

Thus if a sinusoidal feature is detected at location x on the horizontalaxis in a genuine sinusoid a counterpart feature of equal amplitude andopposite sign should exist at location (x+π)^(c). A method that involvessearching at such a location therefore is likely to be a reliable way ofaffirming whether likely sinusoid features indeed are parts ofsinusoids.

However as noted the sinusoids encountered in image logs are alwaysimperfect in the ways outlined hereinabove. It therefore is necessary totake account of the fact that the amplitude and shape of the sinusoid at(x+π)^(c) is unlikely to be a precise mirror image of the waveform atlocation x.

To this end the method of the invention includes the further steps of:

-   -   a. processing the image log data on the basis of a sequential        line-by-line approach in which each line in the image log is        vertically spaced from at least one neighbor;    -   b. at each line analyzing a window of pixels above and below the        line;    -   c. for each pixel position p1 in the window assessing whether        the pixel contains part of an edge feature;    -   d. if the result of Step c is positive, identifying a further        pixel position p2 shifted horizontally by W/2, where W is the        image width, and reflected vertically about the said line; and    -   e. searching a region centered on p2 for further edge features.

In this context the concept of shifting the assessed pixel position byW/2 includes wrapping the pixel position in the event of the shiftotherwise extending beyond the end of the extent of the image in ahorizontal direction. Thus the W/2 shifted position is always somewherein the image.

Preferably the step e. of searching a region centered on pixel positionp2 includes, in respect of each edge feature detected, incrementing anaccumulator relating to the said line; performing a threshold analysison the value of the accumulator; and using the result of the thresholdanalysis to determine whether a sinusoid is present at the position ofthe line.

The method of the invention optionally includes repeating the steps ofany of claims 21 to 26 hereof in respect of further lines of the imagelog.

The steps defined in the immediately preceding sections produce as anoutput the identities of candidate lines that can then be assessed usinga more rigorous (and hence slower) process for determining theparameters of the sinusoids.

This more rigorous aspect of the method of the invention preferablyincludes:

-   -   a. processing the image log data on the basis of a sequential        line-by-line approach in which each line in the image log is        vertically spaced from at least one neighbor;    -   b. at each line analyzing a window of pixels above and below the        line;    -   c. for each pixel position p1 in the window assessing whether        the pixel contains part of an edge feature;    -   d. if the result of Step c is positive, determining the slope of        the edge feature at the location p1;    -   e. identifying a further pixel position p2 shifted horizontally        by W/2, where W is the image width, and reflected vertically        about the said line;    -   f. determining the slope of any edge feature at or near position        p2; and    -   g. if the value of the slope at p2 is equal in magnitude and        opposite in sign to that determined at position p1, incrementing        an accumulator relating to the said line; performing a threshold        analysis on the value of the accumulator; and using the result        of the threshold analysis to determine whether a sinusoid is        present at the position of the said line.

A method of parameterizing one or more sinusoids identified throughpracticing of the methods of any of claims 21 to 28 hereof includes thesteps of:

-   -   a. creating a two-dimensional accumulator space representing a        range of values of A and φ; being respectively the amplitude and        phase angle of the sinusoid;    -   b. analyzing each line of the image log that in accordance with        the steps defined above has been identified as containing a        sinusoid;    -   c. for each said line, analyzing a window of pixels above and        below the line and for each pixel position x, y within the        window that contains an identified part of an edge feature,        determining the local slope of the edge;    -   d. for each said slope, determining estimates of A and φ;    -   e. incrementing the element of the accumulator that corresponds        to the resulting, estimated values of A and φ so as to derive an        accumulated count of different values of A and φ;    -   f. repeating steps a. to e. above in respect of the whole window        and determining the maximum value in the accumulator space and,        if it exceeds a threshold;    -   g. selecting the values of A and φ corresponding to the        accumulator element values that exceed the threshold as values        of A and φ whereby to generate data and/or one or more signals        representative of a parameterized sinusoid.

Preferably the step d. includes determining φ using the expression:

$\varphi = {{\tan^{- 1}\left( \frac{2\pi \; y}{\frac{W{y}}{x}} \right)} - \frac{2\pi \; x}{W}}$

Also preferably the step d. includes determining A using the expression:

$A = \frac{y}{\sin \left( {{2\pi \; {x/W}} + \varphi} \right)}$

The foregoing expressions derive from the identity of sinusoids.

Preferred embodiments of the invention optionally include the steps of:

-   -   a. for each non-zero element in the accumulator space,        determining the corresponding values of A and φ;    -   b. setting a counter to zero;    -   c. analyzing each pixel in the image log corresponding to the        sinusoid specified by (i) the identity of the line under        consideration and (ii) the values of A and φ associated with the        said line;    -   d. determining the slope angle of the sinusoid at each pixel        position;    -   e. for a search region centered on each pixel position,        incrementing the counter by the number of pixels identified as        relating to edge features the local slope angle of which lies        within a threshold of the slope angle determined in step a.;    -   f. repeating steps a. to e. in respect of all pixels identified        as relating to edge features; and    -   g. if the counter value exceeds a threshold, allocating the        resulting values of A and φ as parameters of the sinusoid.

Parameterizing of the sinusoid in accordance with the foregoing stepsallows it to be plotted, displayed and processed. Thus the method of theinvention includes employing the sinusoid the parameters of which resultfrom the foregoing method steps in further processing of the image log.

In more detail, such further processing may include one or more furthersteps selected from superimposing an image of the parameterized sinusoidonto the image log, printing the image log including a superimposedsinusoid, displaying the image log including a superimposed sinusoid,displaying or printing the parameterized sinusoid in the absence ofother image log data and/or utilizing data and/or a signalrepresentative of the parameterized sinusoid in one or more calculationsbased on data of the log image or of another log. The further processingalso may include collating, displaying or operating on statistics suchas the number of sinusoids in a log, sinusoid amplitudes and similarquanta.

The invention furthermore resides in a method of processing geologicalinformation including the steps of operating an image logging tool toenergize a geological formation and thereby generate image log data;processing the image log data in accordance with any of the stepsdefined hereinabove; apparatus including one or more image logging toolsand one or more programmable devices programmed to perform any of themethod steps set out herein; and/or in log data produced in accordancewith any such method step.

BRIEF DESCRIPTION OF THE DRAWINGS

There now follows a description of preferred embodiments of theinvention, by way of non-limiting example, with reference being made tothe accompanying representations in which:

FIG. 1 is a schematic, vertically sectioned representation of part of aresistivity image logging tool;

FIG. 2 is a typical image log showing how bedding and an isolatedfracture commonly appear;

FIG. 3 illustrates the concept of phase congruency with reference tosquare and triangular waves;

FIG. 4 is a polar diagram showing Fourier components at a location in animage log signal plotted head to tail thereby illustrating thederivation of energy, the sum of the Fourier amplitudes and the phasecongruency from study of the Fourier components of the signal;

FIGS. 5 a-5 c show an image log and its pre-processing using a phasecongruency approach, in accordance with an aspect of the invention;

FIGS. 6 a-6 d show respectively an original image (FIG. 6 a) and therendering of image features at (from FIG. 6 b to FIG. 6 d) increasinglyfine scales in accordance with an aspect of the method of the invention,and showing how certain edge features fail to give rise to disconnectededge curves at the finest levels of scale;

FIG. 7 is a flowchart summarizing the pre-processing steps of the methodof the invention in the case of pre-processing being based onestablishing phase congruency:

FIGS. 8 a-8 e show an original image log (FIG. 8 a) and the effects onit of pre-processing in accordance with the steps summarized in FIG. 7;

FIG. 9 is a flowchart summarizing the pre-processing steps of the methodof the invention in the case of pre-processing being based on amulti-scale Lindeberg method:

FIGS. 10 a-10 e show an original image log (FIG. 10 a) and the effectson it of pre-processing in accordance with the steps summarized in FIG.9;

FIG. 11 is a schematic representation of an algorithm, in accordancewith the invention, for detecting the presence of sinusoids in thepresence of noise;

FIGS. 12 a-12 c are, respectively, an extract of original data of animage log; a display of lines at which possible sine waves have beendetected using the relatively fast sinusoid detection steps of themethod of the invention; and the same image, including the estimatedsine waves resulting from the parameterization process steps of theinvention overlain on the candidate lines;

FIGS. 13 a and 13 b are, respectively, the results of sinusoidestimations in which the pre-processing steps are those of the phasecongruency approach (FIG. 13 a) and the gradient-based approach (FIG. 13b) of the invention as defined herein;

FIGS. 14 a and 14 b are similar to FIGS. 13 a and 13 b and show theoutput of the method of the invention when carried out on a differentimage log data set than used in FIGS. 13 a and 13 b;

FIG. 15 shows the result of using a combined pre-processing approach, inaccordance with the invention, on the data set used to generate FIGS. 14a and 14 b;

FIG. 16 is a schematic drawing showing an electronic viewing device forprocessing image log data and nuclear log data according to theinvention; and

FIG. 17 is an example of a GUI that may be used to control the methodsteps of the invention and adjust its parameters.

DETAILED DESCRIPTION OF THE DISCLOSURE

Referring to the representations there are shown effects of methodsaccording to the invention. Before studying the invention in detailhowever it is desirable to review the nature of sinusoids in image logs,and the reasons why they can be problematic to assess.

A. Sinusoid Basics

A planar surface intersecting a cylinder describes a sine wave on thesurface of the cylinder.

The cylinder may be represented (in cylindrical coordinates r, φ and z)by the equation r=R, where R is the radius of the cylinder. Thus anypoint on the cylinder can be represented (in Cartesian coordinates) by(Rcosφ; Rsinφ; z) where φ is the azimuth (angle around the cylinder) andz is the distance of the point along the cylinder axis. To obtain theintersection of a plane with the cylinder, it is necessary to solve theequation of a plane with the cylinder. A plane can be defined using theequation

n. p=o   (1)

where n=(n_(x); n_(y); n_(z)) the unit vector in the directionperpendicular to the plane and p is any point in space. Thus, bysubstituting p=(Rcosφ; Rsinφ; z) in equation (1) and solving for z,

$\begin{matrix}{z = \frac{{{- {Rn}_{x}}\cos \; \varphi} - {{Rn}_{y}\sin \; \varphi}}{n_{z}}} & (2)\end{matrix}$

The normal (unit vector in the direction perpendicular to the plane)n=(n_(x); n_(y); n_(y); n_(z)) may be represented in sphericalcoordinates as

n=(sin φ_(n) cos θ_(n); sin φ_(n) sin θ_(n); cos φ_(n))   (3)

where φ_(n) is the angle made by the normal n with the z-axis and θ_(n)is the angle between the positive x-axis and the projection of thenormal onto the XY-plane.

By substituting (nx; ny; nz)=(sin φ_(n) cos θ_(n); sin φ_(n) sin θ_(n);cos φ_(n)) in equation (2),

z=−R tan φ_(n) cos (φ−φ_(n))   (4)

Thus, z has a sinusoidal curve dependence on the azimuth φ for anintersecting bedding plane. Planar features in a formation can thereforebe detected as sinusoids in the image. However, such features aregenerally not isolated. Fractures, for example, are typically embeddedin a prominent background of bedding planes. The bedding often manifestsitself as stacked sinusoids with common amplitude (resulting from thebedding dip) and phase (resulting from the bedding azimuth). A strategyfor detecting one is unlikely to be appropriate for the other. Fracturesmay be substantially less common than bedding or vice-versa, and mayhave a high apparent dip relative to bedding, making fractures theexceptions where bedding is the rule (and, also, vice-versa). Also,multiple (intersecting) fractures may be present. FIG. 2 shows aborehole image 16 containing bedding 17 and a single fracture 18.

Detection of these sinusoids presents several difficulties. Firstly, theimages suffer a number of distortions, some of which can be identifiedin FIG. 2. Specifically:

-   -   Distortions associated with variations in the speed of the tool    -   The borehole is not perfectly cylindrical    -   Geological boundaries are not perfectly planar    -   Sinusoids may be incomplete due to:        -   Missing information due to partial coverage (that may be            addressed by the aforementioned gap-filling techniques)        -   Fractures being truncated at bed boundaries.

Secondly, the presence of multiple, intersecting curves is a problem forprior art curve detection techniques such as the Radon or Hough methods.Even though the Radon transform is capable of dealing with intersectingcurves, it is necessary first to obtain an edge map. This edge map mustbe able to represent intersecting curves, because if information is lostat this stage it cannot be retrieved at a later stage. This problem istackled by adopting an orientation space approach. However, theparameter space computed by the Radon transform contains a large numberof local maxima which do not correspond to actual sinusoidal events inthe image (despite the orientation constraints). It is possible todistinguish between three types of bad picks (detected curves):

-   -   Picks due to background noise: integration along a curve through        a noisy region results in a significant value in parameter        space.    -   Picks due to connecting segments that belong to different        fractures.    -   Picks due to detecting a single fracture multiple times. For a        correctly picked fracture with amplitude A, curves with slightly        larger or small amplitude still give a good fit on the flanks of        the sinusoid.

The inventors have found that the drawbacks of prior art curve detectiontechniques may be overcome by adopting novel approaches to theidentification of sinusoids. The inventors furthermore have found thatthe success of such novel approaches may be noticeably enhanced bypre-processing the log data, or signals derived from them, as describedin the following sections hereof:

B. Pre-Processing—Edge Detection

The inventors have found that good edge detection is very important ifthe number of false sinusoids is to be kept to a minimum. The commonlyused algorithms are not suitable for this application, so two algorithmshave been developed. They are: gradient and phase-based edge detection.

In the following the phase-based edge detection method is describedfirst. In practical embodiments of the method of the invention one ofthe described edge detection techniques may be practiced on its own; orthey may be used in combination. One effective regime the inventors haveadopted involves firstly carrying out the steps of a gradient-based edgedetection method; and subsequently processing the thus-treated log datausing a phase congruency method. This combination has been found to givegood results.

One major advantage of the phase-based approach versus the classicalgradient-based approach (Sobel, Canny . . . ) is that the resultingcorner and edge operator is highly localized and has responses that areinvariant to image contrast. This results in reliable feature detectionunder a wide range of measurement contrast conditions with fixedthresholds.

C. Phase Congruency

The local energy model of feature detection postulates that features areperceived at points of maximum phase congruency^([1]). For example,considering the Fourier series that makes up a square wave, all theFourier components are sine waves that are exactly in phase at the pointof the step at an angle of 0 or 180 degrees (as represented by FIG. 3which shows the phase congruency of an (i) illustrative square wave(left hand plot) constructed from a number of sine waves and (ii) asimilarly constructed triangular wave (right hand plot)) depending onwhether the step is upward or downward. At all other points in thesquare wave phase congruency is low. Similarly, one finds that phasecongruency is a maximum at the peaks of a triangular wave (at an angleof 90 or 270 deg.). Congruency of phase at any angle produces a clearlyperceived feature.

Morrone & Evans^([2]) define the phase congruency function in terms ofthe Fourier series expansion of a signal at some location x as

$\begin{matrix}{{{PC}(x)} = {\max_{{\overset{\_}{\varphi}{(x)}} \in {\lbrack{0,{2\pi}}\rbrack}}\frac{\sum\limits_{n}{A_{n}{\cos \left( {{\varphi_{n}(x)} - {\overset{\_}{\varphi}(x)}} \right)}}}{\sum\limits_{n}A_{n}}}} & (6)\end{matrix}$

where A_(n) represents the amplitude of the nth Fourier component, andφ_(n)(x) represents the local phase of the Fourier component at positionx. The value of φ(x) that maximizes this equation is the amplitudeweighted mean local phase angle of all the Fourier terms at the pointbeing considered. Taking the cosine of the difference between the actualphase angle of a frequency component and this weighted mean, φ(x),generates a quantity approximately equal to one minus half thisdifference squared (the Taylor expansion of cos(x)≈1−x2/2 for small x).Thus, finding where phase congruency is a maximum is approximatelyequivalent to finding where the weighted variance of local phase angles,relative to the weighted average local phase, is a minimum.

Phase congruency however may be a rather awkward quantity to calculate.As an alternative, Venkatesh and Owens^([3]) show that point of maximumphase congruency can be calculated equivalently by searching for peaksin the local energy function. The local energy function is defined for aone-dimensional luminance profile, I(x), as

E(x)=√{square root over (F ²(x)+H ²(x))}{square root over (F ²(x)+H²(x))}  (7)

where F(x) is the signal I(x) with its DC component removed, and H(x) isthe Hilbert transform of F(x) (a 90 deg. phase shift of F(x)).Typically, approximations to the components F(x) and H(x) are obtainedby convolving the signal with a quadrature pair of filters. It has beenshown by Venkatesh and Owens^([3]) that energy is equal to phasecongruency scaled by the sum of the Fourier amplitudes; that is:

E(x)=PC(x)Σ_(n) A _(n)   (8)

Thus, the local energy function is directly proportional to the phasecongruency function, so peaks in local energy will correspond to peaksin phase congruency. The relationship between phase congruency, energy,and the sum of the Fourier amplitudes can be seen geometrically in FIG.4. The local Fourier components are plotted as complex vectors addinghead to tail. The sum of these components projected onto the real axisrepresents F(x), the original signal with DC component removed; and theprojection onto the imaginary axis represents H(x), the Hilberttransform. The magnitude of the vector from the origin to the end pointis the total energy, E(x). E(x) is equal to Σ_(n) A_(n) cos(φ_(n)(x)−φ(x))

Phase congruency is the ratio of E(x) to the overall path length takenby the local Fourier components in reaching the end point. Thus, it isclear that the degree of phase congruency is independent of the overallmagnitude of the signal. This means that the methods of the inventionprovide invariance to variations in image illumination and/or contrastrelative to the gradient-based techniques.

The calculation of energy from spatial filters in quadrature pairs hasbeen central to many models of human visual perception. Also complexGabor filters can be used to detect edges and bars in images. Prior artworkers have recognized that step edges and bars have specific localphase properties that can be detected using filters in quadrature;however, in contrast to the inventive methods defined and describedherein they have not connected the significance of high local energywith the concept of phase congruency.

FIGS. 5 a-5 c illustrate the effects of phase congruency-basedpre-processing of an image log.

In FIG. 5 a an original borehole image 16 is similar to that of FIG. 2and contains two fractures 18 together with bedding features 17 and asignificant amount of noise, extraneous and partial features and so on.

A human who visually inspects the image of FIG. 5 a can readily discernthe sinusoids representing the fractures 18, but for reasons explainedherein a computer encounters difficulty when seeking to perform the sametask on the untreated image 16.

FIG. 5 b however shows the result of a phase congruency-based approachto edge detection in accordance with an aspect of the invention asdefined herein to produce a pre-processed image 16′. FIG. 5 b reducesthe image essentially to a binary (two contrasting color) one in whichthe edges 18′ representing the sinusoids are much easier for a machinevision analysis program run on a computer to identify.

FIG. 5 c shows a further pre-processed image log 16″ on which techniquesof suppression of non-local maxima and morphological structural elementreconstruction, as described further herein, have been applied. Forreasons explained below the edge features 18″ in this version of theimage are more suitable still for processing by a computer for thepurpose of parameterizing the sinusoids. Similarly the most significantbedding features 17″ in this image are rendered in a format that iseasily detectable by a computer.

Further or alternative pre-processing of image log data in accordancewith a gradient-based approach also yields improvements. Gradient-basedpre-processing is described in the following sections. The inventors arethe first workers to realize that such techniques may be appliedsuccessfully to image log processing.

D. Gradient-Based Edge Detection

Gradient-based edge detection is a process of identifying and locatingsharp discontinuities. These discontinuities are abrupt changes in pixelintensity (amplitude rather than phase) which characterize boundaries ofobjects in a scene. Prior art methods of edge detection involveconvolving the image with an operator (a 2-D filter), designed to besensitive to large gradients while returning values of zero in uniformregions. Numerous edge detection operators are available, each designedto be sensitive to certain types of edges. Variables involved in theselection of an edge detection operator include:

-   -   Edge orientation: The geometry of the operator determines a        characteristic direction in which it is most sensitive to edges.        Operators can be optimized to look for horizontal, vertical, or        diagonal edges.    -   Noise environment: Edge detection is difficult in noisy images,        since both the noise and the edges contain high-frequency        content. Attempts to reduce the noise result in blurred and        distorted edges. Operators used on noisy images are typically        larger in scope, so they can average enough data to discount        localized noisy pixels. This results in less accurate        localization of the detected edges.    -   Edge structure: Not all edges involve a step change in        intensity. Effects such as refraction or poor focus can result        in objects with boundaries defined by a gradual change in        intensity. These assumptions also hold in resistivity images        although they are not optical images. The operator needs to be        chosen to be responsive to such a gradual change in those cases.        Newer wavelet-based techniques characterize the nature of the        transition for each edge in order to distinguish, for example,        edges associated with one feature from those of another.

There are many ways to perform edge detection, but most may be groupedinto two categories: Gradient in which the method detects the edges bylooking for the maximum and minimum in the first derivative of the imageand Laplacian in which method searches for zero crossings in the secondderivative of the image to find edges.

E. The Lindeberg Method

One preferred method in accordance with the invention is the Lindebergmethod which relies on finding edges using the differential geometricsingle-scale edge detector given by Lindeberg^([4]). Lindeberg statesthat when computing descriptors of image data, the type of informationthat can be extracted may be strongly dependent on the scales at whichthe image operators are applied. In this technique the novel concept ofa scale-space edge is introduced, defined as a connected set of pointsin scale-space at which:

-   -   1. the gradient magnitude assumes a local maximum in the        gradient direction, and    -   2. a normalized measure of the strength of the edge response is        locally maximal over scales.

An important consequence of this definition is that it allows the scalelevels to vary along the edge detecting one-dimensional image features,such as edges and ridges. Actually, the choice of scale levels canaffect the result of edge detection. Moreover, different scale levelswill, in general, be needed in different parts of the image.Specifically, coarse scale levels are usually necessary to capturediffuse edges (due to shadows and other “illumination” phenomena). Tocope with this problem, Lindeberg has proposed an extension of thenotion of non-maximum suppression, with the scale dimension includedalready in the edge definition. It is based on the idea that in theabsence of further evidence, scale levels for feature detection can beselected from the scales at which normalized measures of featurestrength assume local maxima over scales. For two specific measures ofedge strength, an immediate consequence of this definition is that finescale levels will be (automatically) selected for sharp edges, andcoarse scales for diffuse edges.

An example shown in FIG. 6 illustrates the concept of edge detectionbased on different scales, and how different types of edge structuresare extracted at different scales. In addition, an edge detector basedon this approach computes a diffuseness estimate at each edge point.Such attribute information constitutes an important clue to the physicalnature of the edge. Another important property of this approach is thatthe scale levels are allowed to vary along the edge, which is essentialto capture edges for which the degree of diffuseness varies along theedge.

F. Non-local Maxima Suppression and Cleaning Edges

The two phase and gradient-based approaches may be carried out aspreliminary steps of edge detection before a sinusoiddetection/estimation process in completed. Smooth and continuous edgesare desirable in order to establish a relationship between multiplepixels before estimating the sine waves. When the edges are fragmented,it is necessary to have a way of establishing which edges can combinetogether to form a sine wave. So usually, whether phase-based orgradient-based edge detection, or indeed a combination of thesepre-processing methods, is completed such steps need to be followed by anon-local maxima suppression strategy. As the results from phase-basedand gradient-based pre-processing are different so also the suppressionof non-local maxima differs in dependence on the pre-processing methodselected.

Suppression in Phase-Based Edge Detection. In the case of a phasecongruency approach, after detecting the phase information from theimage the following additional processes are put into effect in thefollowing order:

-   -   Non-local maxima suppression: consists of performing non-local        maxima suppression on an image using an orientation image (the        output from the phase congruency method steps defined herein).        It is assumed that the orientation image gives feature normal        orientation angles in degrees (0-180). This sub-algorithm uses a        bi-linear interpolation to estimate intensity values at ideal,        real-valued pixel locations on each side of pixels to determine        if they are local maxima.    -   Hysteresis thresholding: this sub-algorithm performs hysteresis        thresholding of an image. All pixels with values above threshold        T1 are marked as edges. All pixels that are connected to points        that have been marked as edges and with values above threshold        T2 are also marked as edges and eight-connectivity is used (i.e.        ignoring the center pixel in a square of nine pixels).    -   Morphological cleaning: consists of removing pixels on the        boundaries of objects without allowing objects to break apart.

FIG. 7 summarizes the pre-processing steps of the method of theinvention in the case of a phase congruency based approach; and FIGS. 8b-8 e illustrate in image logs the effects of Steps 4.1-4.4 respectivelyof FIG. 7 on an original image log 16 visible in FIG. 8 a.

G. Suppression in Gradient-Based Edge Detection

In the case of gradient-based pre-processing approach using amulti-scale Lindeberg method, different steps are involved as shown inFIG. 9.

FIGS. 10 b-10 e illustrate the effects of the different steps summarizedin FIG. 9 on an image log 16 presented in FIG. 10 a.

FIGS. 8 and 10 show that the two pre-processing approaches aredifferent, and the steps involved before sine wave detection occurs arealso different. However, for the sine wave detection aspect of themethod of the invention the algorithm is the same regardless of whethera phase congruency approach or the Lindeberg method is used for edgedetection.

H. Detection/Estimation of Sine Waves in Resistivity Images

This section describes the estimation (or in other wordsparameterization) of sine waves, which is the last step of the method ofthe invention. Sinusoidal features in resistivity and acoustic logimages are characterized by having exactly one period and beinghorizontally oriented. In contrast to previous work in this area, themethod of the invention processes binary edge images to detect thepresence of sine waves. These images are obtained using the phasecongruency and/or gradient methods described above. The simplestapproach would be to perform an exhaustive search of the image byconsidering every possible sine wave at every possible line of the imagewith a suitable metric to determine which sine waves are an adequatefit. In practice, this would be computationally heavy. Hence theinventors have developed a faster, two-step technique.

The approach adopted in accordance with the invention to increase thespeed of operation is to use a fast method for detecting the location ofsine waves prior to any attempt to estimate the sine wave parameters.The relatively fast location method is described in the followingsection, after which is presented a description of the approach used forthe estimation of the sine wave parameters.

I. Sine Wave Detection

The purpose of the sine wave detection step is to come up with a list ofpossible lines in the image which may contain a sine wave—these linesare then passed onto the next section of sine wave estimation which ismore time consuming. Reducing some thresholding parameters will increasethe number of lines for processing by the sine wave estimation code, andincreasing it will reduce them. The reason for this first stage issimply to reduce the number of lines in the image that the more timeconsuming sine wave estimation stage has to process.

The algorithm is based upon the trigonometric identity:

sin(θ)=−sin(θ+π)   (9)

and can be summarized as follows:

-   -   1. Process the image on a line-by-line basis.    -   2. At each line consider a window of pixels above and below the        line. For each pixel position (p1) within this window, if this        pixel position contains part of an edge, determine the position        of a new point (p2) shifted horizontally by W/2 (where W is the        image width) pixels and reflected vertically about the current        line. This is depicted in FIG. 11. Note, the images are        “cylindrical” and hence if the new x-coordinate exceeds the        image width (W), then the position “wraps” around to the start        of the row, i.e. we subtract W from the column.    -   3. A small search region centered on p2 is examined for any        detected edges. A count of the number of edge pixels within this        search region is added to an accumulator for this line position.    -   4. A simple threshold on the accumulator values can be used to        decide whether a sine wave is present at this position.

The algorithm relies upon the fact that the symmetry relationshipbetween points p1 and p2 applies to the sine wave features and ingeneral not to edges relating to other image features. The search regionis required to allow for the fact that in practice the sinusoidalfeatures may not be perfect sine waves due to either a non-circularborehole or non-flat intersecting plane. The algorithm in its above formis seen to work well for relatively clean edge images as depicted inFIG. 10. Hence the described pre-processing steps preceding the sinewave detection are strongly desirable. Indeed in one aspect theinvention resides in the combination of pre-processing, sine wavedetection and sine wave estimation.

The detection problem can be addressed by considering the slope of thesine wave. The slope of a sine wave sin(θ) is simply its derivativecos(θ). There exists a similar trigonometric identity relating theslopes:

cos(θ)=−cos(θ+π)   (10)

Hence one may expect the local slopes at points p1 and p2 to be equal inmagnitude but opposite in sign. An algorithm to estimate the local slopeof edges is also adopted here. This algorithm utilizes a simpleflood-fill algorithm to determine connected pixels within a specifiedneighborhood size and, from these pixels, estimate a least squareslinear fit to estimate the local slope. The most efficient way toachieve this is to create a temporary image in which the pixel valuesare either a sentinel value indicating that there is no edge at thatpixel position in the original image, or the local slope angle estimatedfrom the flood-fill algorithm.

Under this new approach, step 3 of the algorithm becomes:

-   -   A small search region centered on p2 is examined for any        detected edges. A count of the number of edge pixels in this        search region, whose estimates of local slope are within a        threshold of the negative of the slope at point p1, is added to        an accumulator for the this line position.

This algorithm reduces the number of false positives, as there is areduced likelihood of this additional symmetry constraints being foundin the non-sinusoidal edge content.

The algorithm is fast and takes a fraction of a second to process animage of 2 meters, including the estimation of local slopes.

J. Sine Wave Estimation

Having determined which lines in an image are likely to contain sinewaves, it remains to process these lines to estimate the sine waveparameters. A simple expression that can be used to represent the sinewave is given by:

$\begin{matrix}{y = {{Asin}\left( {\frac{2\pi \; x}{W} + \varphi} \right)}} & (11)\end{matrix}$

where x and y are the image pixel position, A is the sine waveamplitude, W is the width of the image and φ is the phase angle.

The above expression can be differentiated to obtain an expression forthe slope of the sine wave at a given position (x, y):

$\begin{matrix}{\frac{y}{x} = {\frac{2\pi \; A}{W}{\cos \left( {\frac{2\pi \; x}{W} + \varphi} \right)}}} & (12)\end{matrix}$

From (11) and (12) φ can be deduced as:

$\begin{matrix}{\varphi = {{\tan^{- 1}\left( \frac{2\pi \; y}{\frac{W{y}}{x}} \right)} - \frac{2\pi \; x}{W}}} & (13)\end{matrix}$

Also the amplitude A can be deduced as:

$\begin{matrix}{A = \frac{y}{\sin \left( {{2\pi \; {x/W}} + \varphi} \right)}} & (14)\end{matrix}$

The algorithm can be summarized as follows:

-   -   1. Create a 2-dimensional accumulator space representing the        range of considered values of A and φ.    -   2. Visit each line in the image in which the sine wave detection        algorithm has indicated that a sine wave may be present.    -   3. At each line consider a window of pixels above and below the        line. For each pixel position (x,y) within this window that        contains part of an edge, determine the local slope of this edge        and hence determine estimates for φ and A from the previous        equations.    -   4. Increment the accumulator element corresponding to the        estimated values of φ and A.    -   5. After processing the entire window, determine the maximum        value in the accumulator space and if it exceeds a suitable        threshold, select the corresponding values of φ and A.

This algorithm is extremely fast and has been demonstrated to work wellfor synthetic images of sine wave edges in the presence of binary noise.However, the performance is significantly degraded for some of the typesof sine wave features found in the resistivity data. This is partly dueto features that are not properly sinusoidal or where the local edgesare jagged leading to errors in the estimates of the edge slope. Theseeffects will combine to lead to a spreading of the estimates of φ and Athat leads to poor peaks in the accumulator space resulting in poor sinewave fits.

In order to compensate for these types of errors, a modified algorithmcan proceed from step 5 as:

-   -   6. For each non-zero element of the accumulator space determine        the corresponding values of A and φ. Initialize a counter to        zero.    -   7. Visit each pixel in the image corresponding to the sine wave        specified by the current line and values of A and φ.    -   8. Determine the slope angle of the actual sine wave at each        pixel position.    -   9. For a small search region centered on each pixel position,        increment the counter by the number of any edge pixels whose        local slope angle lies within a threshold of the actual slope        angle determined in step 6.

Once all pixels in the candidate sine wave have been visited, if thecounter value exceeds a suitable threshold, the corresponding values forA and φ are used to define the sine wave fit.

The use of a threshold in step 9 means that any false positives from thesine wave detection process can be discounted by the estimationalgorithm.

FIG. 12 illustrates the results obtained using this procedure for a realdata set. An extract of this data set is shown in FIG. 12 a where we cansee three possible sine wave features. The results of the sine wavedetection process are depicted in FIG. 12 b as dotted lines overlaid onthe original image representing the center lines of possible sine waves.FIG. 12 c depicts the results of the sine wave estimation process withthe detected sine waves shown overlaid on the original image.

K. Examples of Sine Waves Detection in Resistivity Images

FIG. 13 shows examples on a different data set using the two differentapproaches (phase congruency (FIG. 13 a)/Lindeberg (FIG. 13 b)) for sinewaves detection.

In FIGS. 13 a and 13 b the resistivity image is given and the detectedsinusoid superimposed on top of it.

Experiments completed by the inventors suggested that an approach ofcombining the gradient-based and phase congruency pre-processing stepsmay yield further improved results; and as illustrated in FIG. 15further improvements are available by using the gradient-based approachas the primary sinusoid detection one, and then validating the detectedsinusoids using the phase congruency of the original image.

In order to display and process, as described herein, the image log dataFIG. 16 shows an electronic viewing device 70, such as a computer, thatis used for viewing the image log data 74. The electronic viewing device70 has an input device, such as mouse, keyboard, etc., that is capableof selecting one or more parts of the image log data 74 or performingother, per se known, tasks.

The viewing device 70 includes a display monitor via which a graphicaluser interface (GUI) according to the invention may be viewed and, inconjunction with input devices such as the mouse and keyboard, used toinitiate and/or control parameters of methods in accordance with theinvention. Such parameters as may be varied using the GUI of theinvention include for example the fineness of scale used in theLindeberg edge detection steps described herein; and the thresholdingemployed when selecting candidate lines for sinusoid parameterization.

An exemplary GUI in accordance with the invention is shown in FIG. 17.

Overall the method and apparatuses of the invention represent asignificant step forward in the automation of the detection andestimation of sinusoids in image logs. For the first time such processesmay be carried out rapidly, and using computer processing capacityacceptably economically.

The listing or discussion of an apparently prior-published document inthis specification should not necessarily be taken as an acknowledgementthat the document is part of the state of the art or is common generalknowledge.

L. REFERENCES

-   [1] Peter Kovesi, Image Features from Phase Congruency, Journal of    Computer Vision Research, Summer 1999, Volume 1, Number 3, The MIT    Press.-   [2] M. C. Morrone and R. A. Owens. Feature detection from local    energy. Pattern Recognition Letters, 6:303-313, 1987.-   [3] S. Venkatesh and R. A. Owens. An energy feature detection    scheme. In The International Conference on Image Processing, pages    553-557, Singapore, 1989.-   [4] T. Lindeberg, Edge Detection and Ridge Detection with Automatic    Scale Selection. International Journal of Computer Vision archive,    Volume 30 issue 2, November 1998, Pages 117-156. Further published    documents of potential interest to the reader include:-   D. J. Heeger, Optical flow from spatiotemporal filters. In    Proceedings, 1^(st) International Conference on Computer Vision,    pages 181-190, London, June 1987.-   D. J. Heeger. Optical flow using spatiotemporal filters.    International Journal of Computer Visition, 1:279-302, 1988.-   D. J. Heeger. Normalization of cell responses in cat striate cortex.    Visual Neuroscience, 9:181-197, 1992.-   E. H. Adelson and J. R. Bergen. Spatiotemporal energy models for the    perception of motion. Journal of the Optical Society of America A,    2(2): 284-299, 1985.-   Z. Wang and M. Jenkin. Using complex Gabor filters to detect and    localize edges and bars. In Colin Archibald and Emil Petriu (eds.).-   A. Grossman. Wavelet transforms and edge detection. In S.    Albeverio, P. Blachard, M. Hazewinkel, and I. Streit (eds)    Stochastic Processes in Physics and Engineering, pages 149-157. D.    Reidel Publishing Company, 1988.-   Lim, Jae S., Two-Dimensional Signal and Image Processing, Englewood    Cliffs, N.J., Prentice Hall, 1990, pp. 478-488.-   T. Lindeberg. Discrete derivative approximations with scale-space    properties: A basis for low-level feature extraction. J. of    Mathematical Imaging and Vision, 3(4): 349-376, November 1993.-   T. Lindeberg. Scale-space theory: A basic tool for analysing    structures at different scales. Journal of Applied Statistics,    21(2): 225-270, 1994. Supplement Advances in Applied Statistics:    Statistics and Images.

1. A method of detecting an edge of a geological characteristic in aborehole comprising, in respect of an image log of a length of aborehole, carrying out the steps of a gradient-based edge detectionmethod.
 2. A method according to claim 1 wherein the gradient-based edgedetection method is a differential geometric multi-scale method.
 3. Amethod according to claim 2 including the step of defining as ascale-space edge a set of connected points in a scale-space at which: a.the gradient magnitude assumes a local maximum in the gradientdirection; and b. a normalized measure of the strength of the edgeresponse is locally maximal over plural scales.
 4. A method according toclaim 3 including varying scale levels from place to place along thesaid edge.
 5. A method according to claim 4 wherein the scale levelsemployed for detection of relatively sharper edges are finer than thescale levels employed for detection of relatively less sharp edges.
 6. Amethod according to claim 5 including calculating a diffuseness estimateat each of a plurality of points along the said edge.
 7. A methodaccording to claim 1 including, subsequently, completing one or moresteps selected from the list comprising: (i) removing one or morevertical features resulting from pad normalization anomalies; (ii)operating a Lindeberg edge algorithm (as defined herein) to enhance edgeconnectivity; (iii) breaking of one or more edges that bend back onthemselves in the x-direction; (iv) removing any pixels that areconnected to more than two other pixels; and (v) seeking to remove edgesderived from edge content or edge-type content in background textureforming part of the log. 8-34. (canceled)
 35. A method of according toclaim 1 including the steps of operating an image logging tool toenergize a geological formation and thereby generate image log data ofthe image log; and processing the image log data in accordance withclaim
 1. 36. Apparatus including one or more image logging tools and oneor more programmable devices programmed to perform the method ofclaim
 1. 37. A method of according to claim 1 further comprisingproducing log data in accordance with the method of claim
 1. 38. Amethod according to claim 1 including suppressing non-local maxima.